Op Amps for Everyone - The Repeater Builder's Technical ...

Superposition
2.6 Superposition
Superposition is a theorem that can be applied to any linear circuit. Essentially, when
there are independent sources, the voltages and currents resulting from each source can
be calculated separately, and the results are added algebraically. This simplifies the calculations
because it eliminates the need to write a series of loop or node equations. An
example is shown in Figure 2–11.
R 1
R 2
R 3
V 2
V 1
V OUT
Figure 2–11.Superposition Example
When V 1 is grounded, V 2 forms a voltage divider with R 3 and the parallel combination of
R 2 and R 1 . The output voltage for this circuit (V OUT2 ) is calculated with the aid of the voltage
divider equation (2–23). The circuit is shown in Figure 2–12. The voltage divider rule
yields the answer quickly.
V 2
R 3
R 1 R 2
V OUT2
Figure 2–12. When V 1 is Grounded
V OUT2
V 2
R 1
R 2
R 3
R 1
R 2
(2–23)
Likewise, when V 2 is grounded (Figure 2–13), V 1 forms a voltage divider with R 1 and the
parallel combination of R 3 and R 2 , and the voltage divider theorem is applied again to calculate
V OUT (Equation 2–24).
V 1
R 1
R 3 R 2
V OUT1
Figure 2–13. When V 2 is Grounded
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